From 5ed337b4ac3b30abf751e3f4225e7d1d7b839bf9 Mon Sep 17 00:00:00 2001
From: Matt Murbach <mmurbach@uw.edu>
Date: Mon, 20 Feb 2023 12:36:16 -0800
Subject: [PATCH 1/3] adds B/2 term to Paasch element, fixes #251

---
 impedance/models/circuits/elements.py | 4 ++--
 1 file changed, 2 insertions(+), 2 deletions(-)

diff --git a/impedance/models/circuits/elements.py b/impedance/models/circuits/elements.py
index 9bb860e..65deb6e 100644
--- a/impedance/models/circuits/elements.py
+++ b/impedance/models/circuits/elements.py
@@ -344,7 +344,7 @@ def T(p, f):
     -----
     .. math::
 
-        Z = A\\frac{\\coth{\\beta}}{\\beta} + B\\frac{1}{\\beta\\sinh{\\beta}}
+        Z = A\\frac{\\coth{\\beta}}{\\beta} + B\\frac{1}{\\beta\\sinh{\\beta}} + \\frac{B}{2}
 
     where
 
@@ -377,7 +377,7 @@ def T(p, f):
         else:
             sinh.append(1e10)
 
-    Z = A / (beta * np.tanh(beta)) + B / (beta * np.array(sinh))
+    Z = A / (beta * np.tanh(beta)) + B / (beta * np.array(sinh)) + B / 2
     return Z
 
 

From 5c36be81af77bce50d9dfdd6dbe73f2dd17c3cb5 Mon Sep 17 00:00:00 2001
From: Matt Murbach <mmurbach@uw.edu>
Date: Mon, 20 Feb 2023 12:40:13 -0800
Subject: [PATCH 2/3] update tests for new Paasch equation

---
 impedance/tests/test_circuit_elements.py | 6 +++---
 1 file changed, 3 insertions(+), 3 deletions(-)

diff --git a/impedance/tests/test_circuit_elements.py b/impedance/tests/test_circuit_elements.py
index c481f5b..b7aa086 100644
--- a/impedance/tests/test_circuit_elements.py
+++ b/impedance/tests/test_circuit_elements.py
@@ -59,9 +59,9 @@ def test_each_element():
             (0.35594139 - 0.16491599j),
         ],
         "T": [
-            (1.00041 - 0.00837309j),
-            (0.0156037 - 0.114062j),
-            (0.00141056 - 0.00141039j),
+            (1.10041251-0.00837309j),
+            (0.11560368-0.11406217j),
+            (0.10141056-0.00141039j),
         ],
         "K": [
             (0.099999842086579 - 0.000125663507704j),

From 6a72c280a6111235dcaa24ed1d2f5dffc2a46b77 Mon Sep 17 00:00:00 2001
From: Matt Murbach <mmurbach@uw.edu>
Date: Mon, 20 Feb 2023 12:51:50 -0800
Subject: [PATCH 3/3] break into multiple lines

---
 impedance/models/circuits/elements.py | 3 ++-
 1 file changed, 2 insertions(+), 1 deletion(-)

diff --git a/impedance/models/circuits/elements.py b/impedance/models/circuits/elements.py
index 65deb6e..dc520a9 100644
--- a/impedance/models/circuits/elements.py
+++ b/impedance/models/circuits/elements.py
@@ -344,7 +344,8 @@ def T(p, f):
     -----
     .. math::
 
-        Z = A\\frac{\\coth{\\beta}}{\\beta} + B\\frac{1}{\\beta\\sinh{\\beta}} + \\frac{B}{2}
+        Z = A\\frac{\\coth{\\beta}}{\\beta} + B\\frac{1}{\\beta\\sinh{\\beta}}
+        + \\frac{B}{2}
 
     where